How To Find A Circles Radius

Radius Of A Circle

The radius of a circle is a line segment with ane finish at the eye of the circle, and the other stop on the circle itself. The radius is identified with a lower-case, italic $r$ .

$Radius Of A Circle Definition In Math$

[hide] [evidence]

Radius Of A Circle
Radius Formula
Discover The Radius
- Radius From Circumference
- Radius From Area
- Radius From Diameter
Radius Examples

Radius Of A Circle Formula

The formula y'all use depends on what is known about the circle. Below are three different formulas you can use to find the radius, $r$ , of a circumvolve.

Radius Formulas

If given...	And then...
Circumference (C)	$r = \frac{C}{2 π}$
Area (A)	$r = \sqrt{\frac{A}{π}}$
Bore (d)	$r = \frac{d}{2}$

The relationship between radius and bore is an important one to know when learning to how to summate the radius.

Since the radius is a line segment from the center to the circle, and the diameter, $d$ , is a line segment from on side of a circle through the center of a circle and out to the other side of the circle, it follows that a radius is $\frac{ane}{ii}$ a diameter.

How To Find The Radius Of A Circle

To detect the radius of a circle, plug the given information into the correct formula. You tin find the radius of whatever circumvolve if you lot are given the circumference, area, or diameter.

$Radius Of A Circle Formulas$

How To Discover Radius From Circumference

No affair the size of the circle, the human relationship of the radius to the circumference, $C$ , is a constant, giving united states of america the formula to find radius from circumference:

$How To Find Radius From Circumference$

You can likewise calculate the circumference of a circle with a given radius by using algebra to isolate the $C$ in our formula.

The radius to circumference formula is: $C = 2 π r$

Radius Of Circle From Area

You tin can use the area to find the radius and the radius to find the surface area of a circle. The expanse of a circumvolve is the space it occupies, measured in square units.

Given the area, $A$ , of a circle, its radius is the square root of the area divided by pi:

The formula for radius to surface area is: $A = π r^{2}$

$How To Find Radius From Area$

How To Find Radius From Diameter

If you lot know the bore of a circle, y'all tin can find its radius by dividing the diameter past $ii$ :

This is the simplest formula you tin use to get the radius.

$How To Find Radius From Diameter$

If you need to go from radius to diameter, multiply radius times $2$ : $d = 2 r$

Radius Of A Circle Example

A circumvolve has a diameter of $6 i n c h eastward s$ . What is its radius?
A circle has a radius of $98 f e eastward t$ . What is its bore?
A circle with a circumference of $365 m e t due east r southward$ will accept a radius of how many meters?
A circle with a radius of $11 i due north c h due east southward$ will have a circumference of how many inches?
With a radius of $41 thou m$ , a circle will take an area equal to, what?
What is the radius of the following circle?

$Radius Of A Circle Example Problem$

We don't like to talk in circles, just brand sure y'all work these out earlier checking the answers below!

The radius of a $6 i n c h$ circle is $3 i north c h east due south$ .
A circumvolve has a radius of $98 f e e t$ , then its diameter must be $196 f due east east t$ .
A circumvolve with a circumference of $365 thou due east t e r s$ will have a radius of $58.4 m e t e r s$ .
A circle with a radius of $eleven i n c h e south$ will take a circumference of $69.12 i n c h east due south$ .
With a radius of $41 m i fifty l i k e t e r south$ , a circle volition have an area of roughly $5,281.02 s q u a r eastward m i fifty l i m e t e r s$ or $m m^{2}$ .
The radius of the circle in the epitome above is $75 chiliad$ .